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Power Time Numerical Integration Algorithm for Nonlinear Fractional Differential Equations

Science and Engineering Division, Iwaki Meisei University, 5-5-1 Chuodai lino, Iwaki, Fukushima 970-8551, Japan

Nobuyuki Shimizu

Department of Mechanical Systems and Engineering, Iwaki Meisei University, 5-5-1 Chuodai lino, Iwaki, Fukushima 970-8551, Japan (nshim{at}iwakimu.ac.jp)

A numerical integration algorithm to solve single-degree-of-freedom nonlinear fractional differential equations (NFDEs) is proposed, by introducing the power time concept and by means of the Newmark-β method one step scheme. An NFDE involving fractional derivatives of the displacement and the displacement squared is solved numerically, using the proposed power time algorithm. The error analysis of the algorithm, and the contribution of the displacement squared fractional derivative term to the solution of NFDE, are also given.

Key Words: Fractional differential equation • numerical integration • power time • newmark-β method • nonlinear viscoelasticity • fractional derivative of displacement squared

Journal of Vibration and Control, Vol. 14, No. 9-10, 1313-1332 (2008)
DOI: 10.1177/1077546307087449


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